Meaning of 'stabs-sick eyes'

In this excerpt from Raymond Chandler's Red Wind, I suspect you may have been misled by what looks like a hyphen, but I think is actually an ineptly formatted dash.

I have used curly brackets below to group together what I consider to be the components of the sense units of the sentence in question:

{His eyes moved} {in short stabs} — {sick eyes}.

Chandler's dash introduces a parenthetical description of the man's eyes. It could be rephrased thus:

He moved his sick eyes in short stabs

or

His sick eyes moved in short stabs.

You have mistranscribed this, or drawn from a mistranscribed source. The original has a dash, not a hyphen.

His eyes moved in short stabs—sick eyes.

The basic clause is His eyes moved in short stabs. That is, the direction of his glance moved abruptly from one object to another, as if 'stabbing' the objects viewed. Sick eyes is added to this clause as a further characterization of his eyes: they were 'sick' eyes.